Abstract: An algorithm of predictive sliding mode control based on power-function is designed.This algorithm combines feedback correction with rolling optimization techniques.It not only utilizes global sliding mode surface to design predictive mode of switching function,but also utilizes power-function reaching-law to design referenced track.Theory analysis and numerical simulation both state that this algorithm need not require uncertain supremum of the system and also can retain powerful robustness to uncertain systems dissatisfying matching condition.At the same time,this algorithm can make switch function chattering-freely converge to a certain value which is related with external disturbance.